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Wave power is the capture of energy of
wind wave In fluid dynamics, a wind wave, water wave, or wind-generated water wave, is a surface wave that occurs on the free surface of bodies of water as a result from the wind blowing over the water surface. The contact distance in the direction of t ...
s to do useful
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an animal tr ...
– for example,
electricity generation Electricity generation is the process of generating electric power from sources of primary energy. For electric utility, utilities in the electric power industry, it is the stage prior to its Electricity delivery, delivery (Electric power transmi ...
,
water desalination Desalination is a process that takes away mineral components from saline water. More generally, desalination refers to the removal of salts and minerals from a target substance, as in soil desalination, which is an issue for agriculture. Saltw ...
, or
pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they u ...
ing water. A machine that exploits wave
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
is a wave energy converter (WEC). Waves are generated by wind passing over the sea's surface. As long as the waves propagate slower than the wind speed just above, energy is transferred from the wind to the waves. Air pressure differences between the windward and leeward sides of a wave
crest Crest or CREST may refer to: Buildings *The Crest (Huntington, New York), a historic house in Suffolk County, New York *"The Crest", an alternate name for 63 Wall Street, in Manhattan, New York *Crest Castle (Château Du Crest), Jussy, Switzerla ...
and surface friction from the wind cause
shear stress Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the ot ...
and wave growth. Wave power is distinct from
tidal power Tidal power or tidal energy is harnessed by converting energy from tides into useful forms of power, mainly electricity using various methods. Although not yet widely used, tidal energy has the potential for future electricity generation. Ti ...
, which captures the energy of the current caused by the gravitational pull of the Sun and Moon. Other forces can create
currents Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
, including
breaking waves Breaking or breakin' may refer to: Arts * Breakdancing (also breaking), an athletic style of street dance * ''Breakin, a 1984 American breakdancing-themed musical film * "Breakin, a twelfth-season episode of the American animated television se ...
,
wind Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hou ...
, the
Coriolis effect In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
,
cabbeling Cabbeling is when two separate water parcels mix to form a third which sinks below both parents. The combined water parcel is denser than the original two water parcels. The two parent water parcels may have the same density, but they have diff ...
, and
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
and
salinity Salinity () is the saltiness or amount of salt dissolved in a body of water, called saline water (see also soil salinity). It is usually measured in g/L or g/kg (grams of salt per liter/kilogram of water; the latter is dimensionless and equal ...
differences. As of 2022, wave power is not widely employed for commercial applications, after a long series of trial projects. Attempts to use this energy began in 1890 or earlier, mainly due to its high
power density Power density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volume p ...
. In 2000 the world's first commercial Wave Power Device, the
Islay LIMPET Islay LIMPET was the world's first commercial wave power device and was connected to the United Kingdom's National Grid. History Islay LIMPET (Land Installed Marine Power Energy Transmitter) was developed and operated by Wavegen in cooperatio ...
was installed on the coast of
Islay Islay ( ; gd, Ìle, sco, Ila) is the southernmost island of the Inner Hebrides of Scotland. Known as "The Queen of the Hebrides", it lies in Argyll just south west of Jura, Scotland, Jura and around north of the Northern Irish coast. The isl ...
in Scotland and connected to the National Grid. In 2008, the first experimental multi-generator
wave farm Wave power is the capture of energy of wind waves to do useful work – for example, electricity generation, water desalination, or pumping water. A machine that exploits wave power is a wave energy converter (WEC). Waves are generated by wind ...
was opened in Portugal at the
Aguçadoura Wave Park Aguçadoura is a Portuguese ''freguesia'' ("civil parish") and former civil parish located in Póvoa de Varzim. In the census of 2001, it had a population of 4,530 inhabitants and a total area of 3.47 km2. A 2013 law amalgamated it into the new ...
. Both projects have since ended. Wave energy converters can be classified based on their working principle as either: * oscillating water column (with air turbine) * oscillating bodies (with hydroelectric motor, hydraulic turbine, linear electrical generator) * overtopping (with low-head hydraulic turbine)


History

The first known patent to extract energy from ocean waves was in 1799, filed in Paris by
Pierre-Simon Girard Pierre-Simon Girard (4 November 1765 – 30 November 1836) was a French mathematician and engineer, who worked on fluid mechanics. Girard was born in Caen. A prodigy who invented a water turbine at the age of ten, he worked as an engineer at th ...
and his son. An early device was constructed around 1910 by Bochaux-Praceique to power his house in
Royan Royan (; in the Saintongeais dialect; oc, Roian) is a commune and town in the south-west of France, in the department of Charente-Maritime in the Nouvelle-Aquitaine region. Its inhabitants are known as ''Royannais'' and ''Royannaises''. Capi ...
, France. It appears that this was the first oscillating water-column type of wave-energy device. From 1855 to 1973 there were 340 patents filed in the UK alone. Modern pursuit of wave energy was pioneered by
Yoshio Masuda Yoshio Masuda (died 2009) was a former Japanese naval commander, regarded as the father of modern wave power technology. Among other devices, the now used principle of Oscillating Water Column is regarded as his invention. It was initially used for ...
's 1940s experiments. He tested various concepts, constructing hundreds of units used to power navigation lights. Among these was the concept of extracting power from the angular motion at the joints of an articulated raft, which Masuda proposed in the 1950s. The oil crisis in 1973 renewed interest in wave energy. Researchers re-examined waves' potential to extract energy, notably
Stephen Salter Stephen Hugh Salter, (born 7 December 1938) is Emeritus Professor of Engineering Design at the University of Edinburgh and inventor of the eponymous Salter duck wave energy device. Salter is also a proponent of geoengineering and is responsib ...
,
Johannes Falnes Johannes Falnes (born 15 December 1931) is a Professor Emeritus of Experimental Physics at the Department of Physics of the Norwegian University of Science and Technology noted for his contributions to wave energy research. He is one of the pione ...
, Michael E. McCormick,
David Evans David, Dave, or Dai Evans may refer to: Academics * Sir David Emrys Evans (1891–1966), Welsh classicist and university principal * David Evans (microbiologist) (1909–1984), British microbiologist * David Stanley Evans (1916–2004), British a ...
, Michael French,
Nick Newman Nick Newman (born 17 July 1958) is a satirical British cartoonist and comedy scriptwriter. Early life The son of an RAF officer, Newman was born in Kuala Lumpur and schooled at Ardingly College where his satirical career began, working on ...
, and
C. C. Mei Chiang Chung "CC" Mei (born 4 April 1935) is Ford Professor of Engineering, Emeritus, at the Department of Civil and Environmental Engineering of Massachusetts Institute of Technology, known for his contributions in fluid mechanics with applicati ...
. Salter's 1974 invention became known as Salter's duck or ''nodding duck'', officially the Edinburgh Duck. In small scale tests, the Duck's curved
cam Calmodulin (CaM) (an abbreviation for calcium-modulated protein) is a multifunctional intermediate calcium-binding messenger protein expressed in all eukaryotic cells. It is an intracellular target of the secondary messenger Ca2+, and the bind ...
-like body can stop 90% of wave motion and can convert 90% of that to electricity, giving 81% efficiency. In the 1980s, as oil prices ebbed, wave-energy funding shrank, although, first-generation prototypes were tested.
Climate change In common usage, climate change describes global warming—the ongoing increase in global average temperature—and its effects on Earth's climate system. Climate change in a broader sense also includes previous long-term changes to E ...
later reenergized the field. The world's first wave energy test facility was established in
Orkney Orkney (; sco, Orkney; on, Orkneyjar; nrn, Orknøjar), also known as the Orkney Islands, is an archipelago in the Northern Isles of Scotland, situated off the north coast of the island of Great Britain. Orkney is 10 miles (16 km) north ...
, Scotland in 2003 to kick-start the development of a wave and tidal energy industry. The European Marine Energy Centre(EMEC) supported the deployment of more wave and tidal energy devices than any other single site. EMEC provides a variety of test sites in real sea conditions. Its grid-connected wave test site is situated at Billia Croo, on the western edge of the Orkney mainland, and is subject to the full force of the Atlantic Ocean, recording seas as high as 19 metres. Developers testing at the centre include
Aquamarine Power Aquamarine Power was a wave energy company, founded in 2005 to commercialise the Oyster wave energy converter, a device to capture energy from near-shore waves. The company's head offices were in Edinburgh, Scotland. The company ceased to trade o ...
, Pelamis Wave Power, and ScottishPower Renewables. The £10 million Saltire prize challenge was to be awarded to the first to be able to generate 100 GWh from wave power over a continuous two-year period by 2017 (about 5.7 MW average). According to the president of trade association Ocean Renewable Energy Coalition, “The total potential off the coast of the United States is 252 million megawatt hours a year.” Under the Marine Renewable Energy Research and Development Act of 2007 the United States committed $200 million in federal funds toward wave energy technology to be allocated from 2008 through 2012. The
United States Department of Energy The United States Department of Energy (DOE) is an executive department of the U.S. federal government that oversees U.S. national energy policy and manages the research and development of nuclear power and nuclear weapons in the United Stat ...
(DOE) is responsible for the allocation of $50 million per year for research, development, demonstration and commercial application of ocean energy. In 2008 fourteen groups received funding. The most notable include
Oregon State University Oregon State University (OSU) is a public land-grant, research university in Corvallis, Oregon. OSU offers more than 200 undergraduate-degree programs along with a variety of graduate and doctoral degrees. It has the 10th largest engineering co ...
and the
University of Hawaii A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...
. OSU in partnership with the
University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...
, agreed to create the Northwest National Marine Renewable Energy Center for wave and tidal energy. The University of Hawaii agreed to develop and implement a National Renewable Marine Energy Center in Hawaii. A 2017 study by
Strathclyde University The University of Strathclyde ( gd, Oilthigh Shrath Chluaidh) is a public research university located in Glasgow, Scotland. Founded in 1796 as the Andersonian Institute, it is Glasgow's second-oldest university, having received its royal chart ...
and
Imperial College Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
focused on the failure to develop "market ready" wave energy devices – despite a UK government investment of over £200 million over 15 years. Wave Swell Energy installed an oscillating water column trial unit in the
Bass Strait Bass Strait () is a strait separating the island state of Tasmania from the Australian mainland (more specifically the coast of Victoria, with the exception of the land border across Boundary Islet). The strait provides the most direct waterwa ...
at Grassy,
King Island King Island, Kings Island or King's Island may refer to: Australia * King Island (Queensland) * King Island, at Wellington Point, Queensland * King Island (Tasmania) ** King Island Council, the local government area that contains the Tasmanian is ...
(2019). It completed one year of testing in 2022. It is a one-way design that does not require a reversible blade, reducing costs.Its moving parts sit above the waterline. It can be integrated into
breakwaters A breakwater is a permanent structure constructed at a coastal area to protect against tides, currents, waves, and storm surges. Part of a coastal management system, breakwaters are installed to minimize erosion, and to protect anchorages, h ...
and
seawalls A seawall (or sea wall) is a form of coastal defense constructed where the sea, and associated coastal processes, impact directly upon the landforms of the coast. The purpose of a seawall is to protect areas of human habitation, conservation ...
. Efficiency averaged 45–50%. The system is positioned as offering "
firm power Firm services, also called uninterruptible services, are services, such as electricity (firm power) and natural gas supplies, that are intended to be available at all times during a period covered by an agreement. Also, the service is not subject to ...
" that is not dependent on intermittent solar and wind sources. Irish company OceanEnergy's OE35 project is the world's largest floating wave energy device. The company's test machine measures 125 x 59 ft (38.1 x 18 m), drafting 31 ft (9.4 m) weighing 826 tons. The machine is moored to the bottom and captures energy from the fising and falling water levels. The Wells turbine, invented in Belfast in the late 70s uses symmetrically-designed fan blades that convert air coming in either direction into the same direction of rotation. The turbine turns continuously in one direction as the air cycles in and out. OceanEnergy collaborates with 14 partners. Co-funded by the EU Horizon Europe Programme and Innovate UK, the €19.6-million (US$19.3-million) WEDUSEA project is scheduled in three phases over four years. * Design and build an OE35 rig tailored to the conditions at the European Marine Energy Test Site. * Install and test the machine over two years. * Disseminate the results and commercialize the technology at scale.


Physical concepts

Like most fluid motion, the interaction between ocean waves and energy converters is a high-order nonlinear phenomenon. It is described using the incompressible Navier-Stokes equations \begin \frac+(\vec\cdot\vec)\vec&=\nu\Delta\vec+\frac \\ \vec\cdot\vec&=0 \end where \vec u(t, x, y, z) is the fluid velocity, p is the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, \rho the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
, \nu the
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
, and \vec the net external force on each fluid particle (typically
gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
). Under typical conditions, however, the movement of waves is described by
Airy wave theory In fluid dynamics, Airy wave theory (often referred to as linear wave theory) gives a linearised description of the propagation of gravity waves on the surface of a homogeneous fluid layer. The theory assumes that the fluid layer has a uniform mea ...
, which posits that * fluid motion is roughly
irrotational In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not c ...
, * pressure is approximately constant at the water surface, and * the
seabed The seabed (also known as the seafloor, sea floor, ocean floor, and ocean bottom) is the bottom of the ocean. All floors of the ocean are known as 'seabeds'. The structure of the seabed of the global ocean is governed by plate tectonics. Most of ...
depth is approximately constant. The most controversial of these assumptions is the second; surface tension effects are negligible only for wavelengths above a few
decimetre The decimetre (symbol dm) or decimeter (American English) is a unit of length in the International System of Units (SI), equal to one tenth of a metre, ten centimetres, 100 millimetres or 3.937 inches. The common non-SI metric unit of volume, ...
s.


Airy equations

The first condition implies that the motion can be described by a velocity potential \phi(t,x,y,z): \Leftrightarrow\textwhich must satisfy the
Laplace equation In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as \nabla^2\! f = 0 or \Delta f = 0, where \Delta = \nab ...
, \nabla^2\phi=0\textIn an ideal flow, the viscosity is negligible and the only external force acting on the fluid is the earth gravity \vec=(0,0,-\rho g). In those circumstances, the Navier-Stokes equations reduces to +\vec \nabla\bigl(\vec\nabla\phi\bigr)^2= -\cdot\vec\nabla p +\vec\nabla\bigl(\rho gz\bigr), which integrates (spatially) to the Bernoulli conservation law:+\bigl(\vec\nabla\phi\bigr)^2 + p + gz=(\text)\text


Linear potential flow theory

When considering small amplitude waves and motions, the quadratic term \left(\vec\phi\right)^2 can be neglected, giving the linear Bernoulli equation,+ p + gz=(\text)\text and third Airy assumptions then imply\begin & + g=0\quad\quad\quad(\text) \\ &=0\phantom\,\,\quad\quad\quad(\text) \end These constraints entirely determine
sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in m ...
wave solutions of the form \phi=A(z)\sin\text where k determines the
wavenumber In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temp ...
of the solution and A(z) and \omega are determined by the boundary constraints (and k ). Specifically,\begin &A(z)= \\ &\omega=gk\tanh(kh)\text \end The surface elevation \eta can then be simply derived as \eta=-=\cos(kx-\omega t)\text a plane wave progressing along the x-axis direction.


Consequences

Oscillatory motion Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
is highest at the surface and diminishes exponentially with depth. However, for
standing waves In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect ...
(
clapotis In hydrodynamics, a clapotis (from French for "lapping of water") is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a breakwater, seawall or steep ...
) near a reflecting coast, wave energy is also present as pressure oscillations at great depth, producing
microseism In seismology, a microseism is defined as a faint earth tremor caused by natural phenomena. Sometimes referred to as a "hum", it should not be confused with the anomalous acoustic phenomenon of the same name. The term is most commonly used to ref ...
s. Pressure fluctuations at greater depth are too small to be interesting for wave power. The behavior of Airy waves offers two interesting regimes: water deeper than half the wavelength, as is common in the sea and ocean, and shallow water, with wavelengths larger than about twenty times the water depth. Deep waves are dispersionful: short-wavelength waves propagate faster and tend to outpace those with longer-wavelengths. Deep-water group velocity is half the
phase velocity The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...
. Shallow water waves are dispersionless: group velocity is equal to phase velocity, and
wavetrain In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of diff ...
s propagate undisturbed. See page 64–65. The following table summarizes the behavior of waves in the various regimes:


Wave power formula

In deep water where the water depth is larger than half the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, the wave
energy flux Energy flux is the rate of transfer of energy through a surface. The quantity is defined in two different ways, depending on the context: # Total rate of energy transfer (not per unit area); SI units: W = J⋅s−1. # Specific rate of energy transfe ...
isThe energy flux is P = \tfrac \rho g H_^2 c_g, with c_g the group velocity, see The group velocity is c_g=\tfracT, see the collapsed table "''Properties of gravity waves on the surface of deep water, shallow water and at intermediate depth, according to linear wave theory''" in the section "'' Wave energy and wave energy flux''" below. : P = \frac H_^2 T_e \approx \left(0.5 \frac \right) H_^2\; T_e, with ''P'' the wave energy flux per unit of wave-crest length, ''H''''m0'' the
significant wave height In physical oceanography, the significant wave height (SWH, HTSGW or ''H''s) is defined traditionally as the mean ''wave height'' (trough to crest) of the highest third of the waves (''H''1/3). Nowadays it is usually defined as four times the st ...
, ''T''''e'' the wave energy
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
, ''ρ'' the water
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
and ''g'' the acceleration by gravity. The above formula states that wave power is proportional to the wave energy period and to the
square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...
of the wave height. When the significant wave height is given in metres, and the wave period in seconds, the result is the wave power in kilowatts (kW) per metre of
wavefront In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal freque ...
length. For example, consider moderate ocean swells, in deep water, a few km off a coastline, with a wave height of 3 m and a wave energy period of 8 s. Solving for power produces : P \approx 0.5 \frac (3 \cdot \text)^2 (8 \cdot \text) \approx 36 \frac, or 36 kilowatts of power potential per meter of wave crest. In major storms, the largest offshore waves are about 15 meters high and have a period of about 15 seconds. According to the above formula, such waves carry about 1.7 MW of power across each meter of wavefront. An effective wave power device captures a significant portion of the wave energy flux. As a result, wave heights diminish in the region behind the device.


Energy and energy flux

In a
sea state In oceanography, sea state is the general condition of the free surface on a large body of water—with respect to wind waves and swell—at a certain location and moment. A sea state is characterized by statistics, including the wave height, p ...
, the
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the ''arithme ...
energy density In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or . Often only the ''useful'' or extract ...
per unit area of
gravity wave In fluid dynamics, gravity waves are waves generated in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere ...
s on the water surface is proportional to the wave height squared, according to linear wave theory: :E=\frac\rho g H_^2, Here, the factor for random waves is , as opposed to for periodic waves – as explained hereafter. For a small-amplitude sinusoidal wave \eta = a \cos 2\pi\left(\frac-\frac\right) with wave amplitude a, the wave energy density per unit horizontal area is E=\frac\rho g a^2, or E=\frac\rho g H^2 using the wave height H = 2a for sinusoidal waves. In terms of the variance of the surface elevation m_0 = \sigma_\eta^2 = \overline = \fraca^2, the energy density is E=\rho g m_0. Turning to random waves, the last formulation of the wave energy equation in terms of m_0 is also valid (Holthuijsen, 2007, p. 40), due to
Parseval's theorem In mathematics, Parseval's theorem usually refers to the result that the Fourier transform is unitary; loosely, that the sum (or integral) of the square of a function is equal to the sum (or integral) of the square of its transform. It originates ...
. Further, the
significant wave height In physical oceanography, the significant wave height (SWH, HTSGW or ''H''s) is defined traditionally as the mean ''wave height'' (trough to crest) of the highest third of the waves (''H''1/3). Nowadays it is usually defined as four times the st ...
is ''defined'' as H_ = 4\sqrt, leading to the factor in the wave energy density per unit horizontal area.
where ''E'' is the mean wave energy density per unit horizontal area (J/m2), the sum of
kinetic Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory of gases, Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to i ...
and
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
density per unit horizontal area. The potential energy density is equal to the kinetic energy, both contributing half to the wave energy density ''E'', as can be expected from the
equipartition theorem In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. T ...
. The waves propagate on the surface, and the energy is transported horizontally with the
group velocity The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middl ...
. The mean transport rate of the wave energy through a vertical
plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * Planes (gen ...
of unit width, parallel to a wave crest, is the energy
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
(or wave power, not to be confused with the output produced by a device), and is equal to: :P = E\, c_g, with ''cg'' the group velocity (m/s). Due to the
dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given the d ...
for waves under gravity, the group velocity depends on the wavelength ''λ'', or equivalently, on the wave
period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Periodic sentence (or rhetorical period), a concept ...
''T''.
Wave height In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighboring trough. ''Wave height'' is a term used by mariners, as well as in coastal, ocean and naval engineering. At sea, the term ' ...
is determined by wind speed, the length of time the wind has been blowing, fetch (the distance over which the wind excites the waves) and by the
bathymetry Bathymetry (; ) is the study of underwater depth of ocean floors (''seabed topography''), lake floors, or river floors. In other words, bathymetry is the underwater equivalent to hypsometry or topography. The first recorded evidence of water de ...
(which can focus or disperse the energy of the waves). A given wind speed has a matching practical limit over which time or distance do not increase wave size. At this limit the waves are said to be "fully developed". In general, larger waves are more powerful but wave power is also determined by wave speed,
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
, and water
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
.


Wave energy converters

Wave energy converters (WECs) are generally categorized by the method, by location and by the
power take-off A power take-off or power takeoff (PTO) is one of several methods for taking power from a power source, such as a running engine, and transmitting it to an application such as an attached implement or separate machine. Most commonly, it is a sp ...
system. Locations are shoreline, nearshore and offshore. Types of power take-off include:
hydraulic ram A hydraulic ram, or hydram, is a cyclic water pump powered by hydropower. It takes in water at one "hydraulic head" (pressure) and flow rate, and outputs water at a higher hydraulic head and lower flow rate. The device uses the water hammer ef ...
, elastomeric hose pump, pump-to-shore, hydroelectric turbine, air turbine, and linear electrical generator. The four most common approaches are: * point absorber buoys * surface attenuators * oscillating water columns * overtopping devices


Point absorber buoy

This device floats on the surface, held in place by cables connected to the seabed. The point-absorber has a device width much smaller than the incoming wavelength λ. Energy is absorbed by radiating a wave with destructive interference to the incoming waves. Buoys use the swells' rise and fall to generate electricity directly via linear generators, generators driven by mechanical linear-to-rotary converters, or hydraulic pumps. Energy extracted from waves may affect the shoreline, implying that sites should remain well offshore.


Surface attenuator

These devices use multiple floating segments connected to one another. They are oriented perpendicular to incoming waves. A flexing motion is created by swells, and that motion drives hydraulic pumps to generate electricity.


Oscillating wave surge converter

These devices typically have one end fixed to a structure or the seabed while the other end is free to move.
Energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
is collected from the relative motion of the body compared to the fixed point. Converters often come in the form of floats, flaps, or membranes. Some designs incorporate
parabolic reflector A parabolic (or paraboloid or paraboloidal) reflector (or dish or mirror) is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface generated ...
s to focus energy at the point of capture. These systems capture energy from the rise and fall of waves.


Oscillating water column

Oscillating water column Oscillating water columns (OWCs) are a type of wave energy converter that harness energy from the oscillation of the seawater inside a chamber or hollow caused by the action of waves. OWCs have shown promise as a renewable energy source with low e ...
devices can be located onshore or offshore. Swells compress air in an internal chamber, forcing air through a turbine to create
electricity Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
. Significant noise is produced as air flows through the turbines, potentially affecting nearby
birds Birds are a group of warm-blooded vertebrates constituting the class Aves (), characterised by feathers, toothless beaked jaws, the laying of hard-shelled eggs, a high metabolic rate, a four-chambered heart, and a strong yet lightweigh ...
and
marine organisms Marine life, sea life, or ocean life is the aquatic plant, plants, aquatic animal, animals and other organisms that live in the seawater, salt water of seas or oceans, or the brackish water of coastal estuary, estuaries. At a fundamental leve ...
. Marine life could possibly become trapped or entangled within the air chamber. It draws energy from the entire water column.


Overtopping device

Overtopping devices are long structures that use wave velocity to fill a reservoir to a greater water level than the surrounding ocean. The potential energy in the reservoir height is captured with low-head turbines. Devices can be on- or offshore.


Submerged pressure differential

Submerged pressure differential based converters use flexible (typically reinforced rubber) membranes to extract wave energy. These converters use the difference in pressure at different locations below a wave to produce a pressure difference within a closed power take-off hydraulic system. This pressure difference is usually used to produce flow, which drives a turbine and electrical generator. Submerged pressure differential converters typically use flexible membranes as the working surface between the water and the power take-off. Membranes are pliant and low mass, which can strengthen coupling with the wave's energy. Their pliancy allows large changes in the geometry of the working surface, which can be used to tune the converter for specific wave conditions and to protect it from excessive loads in extreme conditions. A submerged converter may be positioned either on the seafloor or in midwater. In both cases, the converter is protected from water impact loads which can occur at the
free surface In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in ...
. Wave loads also diminish in
non-linear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
proportion to the distance below the free surface. This means that by optimizing depth, protection from extreme loads and access to wave energy can be balanced.


Floating in-air converters

Floating in-air converters potentially offer increased reliability because the device is located above the water, which also eases inspection and maintenance. Examples of different concepts of floating in-air converters include: * roll damping energy extraction systems with turbines in compartments containing sloshing water * horizontal axis pendulum systems * vertical axis pendulum systems


Environmental effects

Common environmental concerns associated with
marine energy Marine energy or marine power (also sometimes referred to as ocean energy, ocean power, or marine and hydrokinetic energy) refers to the energy carried by ocean waves, tides, salinity, and ocean thermal energy, ocean temperature differences. The ...
include: * The effects of
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
s and underwater noise; * Physical presence's potential to alter the behavior of marine mammals, fish, and
seabird Seabirds (also known as marine birds) are birds that are adapted to life within the marine environment. While seabirds vary greatly in lifestyle, behaviour and physiology, they often exhibit striking convergent evolution, as the same enviro ...
s with attraction, avoidance, entanglement * Potential effect on marine processes such as
sediment transport Sediment transport is the movement of solid particles (sediment), typically due to a combination of gravity acting on the sediment, and/or the movement of the fluid in which the sediment is entrained. Sediment transport occurs in natural system ...
and
water quality Water quality refers to the chemical, physical, and biological characteristics of water based on the standards of its usage. It is most frequently used by reference to a set of standards against which compliance, generally achieved through tr ...
. * Foundation/mooring systems can affect
benthic organism Benthos (), also known as benthon, is the community of organisms that live on, in, or near the bottom of a sea, river, lake, or stream, also known as the benthic zone.Electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transd ...
effects produced from
subsea power cable A submarine power cable is a transmission cable for carrying electric power below the surface of the water.temperate zones In geography, the temperate climates of Earth occur in the middle latitudes (23.5° to 66.5° N/S of Equator), which span between the tropics and the polar regions of Earth. These zones generally have wider temperature ranges throughout t ...
have the best sites for capturing wave power. The prevailing
westerlies The westerlies, anti-trades, or prevailing westerlies, are prevailing winds from the west toward the east in the middle latitudes between 30 and 60 degrees latitude. They originate from the high-pressure areas in the horse latitudes and trend to ...
in these zones blow strongest in winter. The
National Renewable Energy Laboratory The National Renewable Energy Laboratory (NREL) in the US specializes in the research and development of renewable energy, energy efficiency, energy systems integration, and sustainable transportation. NREL is a federally funded research and d ...
(NREL) estimated the wave energy potential for various countries. It estimated that the US' potential was equivalent to 1170 TWh per year or almost 5% of the country's energy consumption. The Alaska coastline accounted for ~50% of the total. NREL reported that WECs can reach efficiencies near 50%. One study analyzed small devices, reminiscent of buoys, finding them capable of generating upwards of 6 MW of power for a roughly cylindrical 21 kg buoy. Later research points to even smaller versions of WECs that could produce the same amount of energy using roughly one-half of the area as current devices.


Challenges

Environmental impacts must be addressed. Socio-economic challenges include the displacement of commercial and recreational fishermen, and may present navigation hazards. Supporting infrastructure, such as grid connections, must be provided. Commercial WECs have not always been successful. In 2019, for example, Seabased Industries AB in Sweden was liquidated due to "extensive challenges in recent years, both practical and financial".


Wave farms

A wave farm (wave power farm or wave energy park) is a group of colocated wave energy devices. The devices interact hydrodynamically and electrically, according to the number of machines, spacing and layout, wave climate, coastal and benthic geometry, and control strategies. The design process is a multi-
optimization problem In mathematics, computer science and economics, an optimization problem is the problem of finding the ''best'' solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables ...
seeking high power production, low costs and limited power fluctuations.


Gallery of wave energy installations


Patents


WIPO patent application WO2016032360
— 2016 ''Pumped-storage system'' – "Pressure buffering hydro power" patent application * — 2011 ''Ocean wave energy harnessing device'' – Pelamis/Salter's Duck Hybrid patent * — 1974 ''Apparatus and method of extracting wave energy'' – The original "Salter's Duck" patent * — 1977 ''Apparatus for use in the extraction of energy from waves on water'' – Salter's method for improving "duck" efficiency * — 1999 ''Piezoelectric rotary electrical energy generator'' * — 1932 ''Wave Motor'' - Parsons Ocean Power Plant - Herring Cove Nova Scotia - March 1925. The world's first commercial plant to convert ocean wave energy into electrical power. Designer - Osborne Havelock Parsons - born in 1873 Petitcodiac, New Brunswick.
Wave energy converters utilizing pressure differences US 20040217597 A1
— 2004 ''Wave energy converters utilizing pressure differences'' An UK-based company has developed a Waveline Magnet that can achieve a
levelized cost of electricity The levelized cost of electricity (LCOE), or levelized cost of energy, is a measure of the average net present cost of electricity generation for a generator over its lifetime. It is used for investment planning and to compare different methods ...
of £0.01/kWh with minimal levels of maintenance.


See also

*
List of wave power stations The following page lists most power stations that run on wave power. Wave farms are classified into 8 types based on the technology used, such as Surface-following attenuator, Point absorber, Oscillating wave surge converter, Oscillating water co ...
* List of wave power projects *
Wave power in Australia Wave power in Australia is being developed as the country has a long and largely deep-water coastline. It is one of several regions of the world where wave power projects are being considered. Australia has great potential for wave energy because ...
*
Wave power in New Zealand New Zealand has large ocean energy resources but does not yet generate any power from them. TVNZ reported in 2007 that over 20 wave and tidal power projects are currently under development. However, not a lot of public information is available a ...
* Wave power in Scotland *
Wave power in the United States Wave power in the United States is under development in several locations off the east and west coasts as well as Hawaii. It has moved beyond the research phase and is producing reliable energy for the Grid. Its use to-date has been for situations ...
*
Marine energy Marine energy or marine power (also sometimes referred to as ocean energy, ocean power, or marine and hydrokinetic energy) refers to the energy carried by ocean waves, tides, salinity, and ocean thermal energy, ocean temperature differences. The ...
*
Ocean thermal energy conversion Ocean Thermal Energy Conversion (OTEC) uses the ocean thermal gradient between cooler deep and warmer shallow or surface seawaters to run a heat engine and produce useful work, usually in the form of electricity. OTEC can operate with a very hi ...
*
Office of Energy Efficiency and Renewable Energy The Office of Energy Efficiency and Renewable Energy (EERE) is an office within the United States Department of Energy. Formed from other energy agencies after the 1973 energy crisis, EERE is led by the Assistant Secretary of Energy Efficiency an ...
(OEERE) *
World energy consumption World energy supply and consumption is global production and preparation of fuel, generation of electricity, energy transport, and energy consumption. It is a basic part of economic activity. It includes heat, but not energy from food. This art ...


Notes


References


Further reading

*, 431 pp. *, 288 pp. *, 256 pp. *, 601 pp.


External links

*
"Wave Power: The Coming Wave"
from the Economist, June 5, 2008
Tethys
– the Tethys database from the
Pacific Northwest National Laboratory Pacific Northwest National Laboratory (PNNL) is one of the United States Department of Energy national laboratories, managed by the Department of Energy's (DOE) Office of Science. The main campus of the laboratory is in Richland, Washington. O ...
* {{physical oceanography Bright green environmentalism Energy conversion Power station technology Sustainable technologies